JPanel: automatically paint at creation?
private class RadarPanel extends JPanel {
        public RadarPanel() {
            super();
            this.repaint();
        }

        @Override
        public void paintComponent(Graphics g) {
            super.paintComponent(g);

            //painting logic here

            //repaint in 500 ms
            this.repaint(500);
        }
    }

import java.awt.Color;
import java.awt.Dimension;
import java.awt.Graphics;
import java.awt.event.WindowAdapter;
import java.awt.event.WindowEvent;
import java.util.ArrayList;

import javax.swing.JFrame;
import javax.swing.JPanel;

public class PlayerRadar extends JFrame {
    private static final long serialVersionUID = 230324190;

    //settings
    private static final int windowWidth = 300;
    private static final int windowHeight = 300;
    private static final int maxDistance = 250;

    //components
    private PlayerRadar radarWindow;
    private JPanel radarPanel;

    public PlayerRadar(String title) {
        super(title);

        //set reference
        radarWindow = this;

        //create radar window
        Dimension screenSize = java.awt.Toolkit.getDefaultToolkit().getScreenSize();
        this.setAlwaysOnTop(true);
        this.setBackground(new Color(0xFFFFFF));
        this.setBounds(screenSize.width - windowWidth, 0, windowWidth, windowHeight);
        this.addWindowListener(new WindowAdapter() {
            public void windowClosing(WindowEvent e) {
                radarWindow.setVisible(false);
            }
        });
        this.setVisible(true);

        //create a JPanel for drawing
        radarPanel = new RadarPanel();
        radarPanel.setBounds(0, 0, windowWidth, windowHeight);
        radarPanel.setBackground(new Color(0xFFFFFF));

        //add to frame
        this.getContentPane().add(radarPanel);
    }

    private class RadarPanel extends JPanel {
        private static final long serialVersionUID = 230324191;
        private static final int repaintInterval = 500;

        public RadarPanel() {
            super();
        }

        @Override
    public void paint(Graphics g) {
        super.paint(g);

        //draw player oval (center of the frame)
        g.setColor(Color.BLUE); //blue
        int ovalWidth = (int) Math.round(this.getWidth() / 30);
        int ovalHeight = (int) Math.round(this.getHeight() / 30);
        int playerLocalX = (int) Math.round(this.getWidth() / 2);
        int playerLocalY = (int) Math.round(this.getHeight() / 2);
        int ovalX = playerLocalX - ovalWidth / 2;
        int ovalY = playerLocalY - ovalHeight / 2;
        g.fillOval(ovalX, ovalY, ovalWidth, ovalHeight);
        g.setColor(Color.BLACK); //black
        g.drawOval(ovalX, ovalY, ovalWidth, ovalHeight);

        //get info of the player itself
        PlayerInfo thisPlayer = GameUtil.getPlayerInfo();
        float playerPosZ = thisPlayer.position[0];
        float playerPosX = thisPlayer.position[2];
        //float playerRotRad = thisPlayer.rotation;

        //set rectangle specs
        int rectWidth = this.getWidth() / 40;
        int rectHeight = this.getWidth() / 40;

        //only continue if we have information about our player
        if (thisPlayer != null) {
            //get nearby players
            ArrayList<PlayerInfo> playersInfo = GameUtil.getNearbyPlayers();

            //for each other player, draw a rectangle
            for (PlayerInfo playerInfo : playersInfo) {
                //get data
                float posZ = playerInfo.position[0];
                float posX = playerInfo.position[2];
                //float rotRad = playerInfo.rotation;

                //calculate relative x and y
                int rectX = playerLocalX + Math.round((posX - playerPosX) / maxDistance * this.getWidth() / 2) - rectWidth / 2;
                int rectY = playerLocalY + ovalHeight / 2 + Math.round((playerPosZ - posZ) / maxDistance * this.getHeight() / 2)  - rectHeight / 2;

                //draw rectangle
                g.setColor(Color.RED);
                g.fillRect(rectX, rectY, rectWidth, rectHeight);
                g.setColor(Color.BLACK);
                g.drawRect(rectX, rectY, rectWidth, rectHeight);
            }
        }

        //repaint soon
        this.repaint(repaintInterval);
    }
    }
}